Natural parameter
From Encyclopedia of Mathematics
on a rectifiable curve
A parameter 
for a curve 
with parametric representation 
such that the arc length on the curve between two points 
and 
is equal to 
. The parametrization of a curve by the natural parameter is known as its natural parametrization. The natural parametrization of a 
-times differentiable (analytic) curve with no singular points is also 
times differentiable (analytic).
Comments
See also (the references to) Natural equation.
How to Cite This Entry:
Natural parameter. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Natural_parameter&oldid=13269
Natural parameter. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Natural_parameter&oldid=13269
This article was adapted from an original article by D.D. Sokolov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article